Question:
If $A+B=90^{\circ}$ and $\tan A=\frac{3}{4}$, what is $\cot B ?$
Solution:
Given in question:
$A+B=90^{\circ}$
$\tan A=\frac{3}{4}$
$A+B=90^{\circ}$
$\Rightarrow B=90^{\circ}-A$
$\Rightarrow \cot B=\cot \left(90^{\circ}-A\right)$
$\Rightarrow \cot B=\tan A$
$\Rightarrow \cot B=\frac{3}{4}\left[\cot \left(90^{\circ}-A\right)=\tan A\right]$
Hence the value of $\cot B$ is $\frac{3}{4}$
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